K K VERMA and K R SONI
Microwave Laboratory, Department of Physics, Malaviya National Institute of Technology, Jaipur 302 017, India
E-mail: kkvermaphd@rediffmail.com
MS received 25 February 2004; revised 14 July 2004; accepted 27 August 2004
Abstract. The radiation properties of 2×2 element planar array of equilateral triangular patch microstrip antenna in plasma medium are studied. The array factor and far-zone EM-mode and P-mode radiation fields of the array geometry are derived using vector wave function techniques and pattern multiplication approaches. The total field patterns and various characteristics of pattern such as half power beam width (HPBW), first null beam width (FNBW) and direction of maximum radiation are computed for two different values of progressive phase excitation difference between the elements. The results of this array geometry are obtained both in plasma medium and in free space and compared with those of single element equilateral triangular patch microstrip antenna.
Keywords. Microstrip planar array; radiation properties; plasma.
PACS Nos 84.40.Gf; 52.40.Fd; 84.40.Ba
1. Introduction
Due to many unique and attractive properties like light weight, flat profile, low manufacturing cost, compatibility with integrated circuit and better aerodynamics, microstrip antennas and their arrays are becoming increasingly popular in high- performance aircraft, spacecraft, satellite and missile applications [1–4].
The planar array antennas find wide applications in tracking radar, search radar, remote sensing, communications and many others. Planar arrays are more versa- tile and can provide more symmetrical patterns with lower side lobes. In addition, they can be used to scan the main beam of the antenna toward any point in space.
Microstrip planar array antennas mounted on such aerospace vehicles encounter plasma medium during their travel in space, as a result of which radiation prop- erties are altered significantly. This change is caused due to the generation of electroacoustic waves in addition to electromagnetic waves [5,6].
Figure 1. Configuration and coordinate system of 2×2 element planar array of equilateral triangular patch microstrip antenna.
2. Radiation field expressions
The geometry and coordinates system of planar array antenna are shown in figure 1. It consists of four identical triangular microstrip patch element of arm lengtha, on a dielectric substrate of thickness h and substrate permittivity εr. The array element which are positioned alongx-axis are separated by a distancedxand, those alongy-axis are separated by a distancedy. Each patch can be excited by a co-axial feed line from its corner. Among the various modes that may be excited in such disc resonators, we have considered TMnm mode with respect to z-axis. Here n and mare the mode numbers associated with thexand y directions respectively.
TheEz component of field inside the cavity for dominant mode is given as Ez=A1,0,−1[2 cos (2πx/√3a+ 2π/3)·cos (2πy/3a) + cos(4πy/3a)].
(1) For the case of 2×2 element planar array of equilateral triangular patch microstrip antenna, the EM- andP-mode fields are given as
EM-mode
Eθt=−¡η0ω0·[Fx·cosθ·cosφ+Fy·cosθ·sin φ]
×1
4× sin (ψx)
sin (ψx/2)× sin (ψy)
sin (ψy/2), (2)
Eφt=−¡η0ω0·[−Fx·sinφ+Fy·cosφ]
×1
4 × sin(ψx)
sin(ψx/2) × sin(ψy)
sin(ψy/2). (3)
Figure 2. E-plane radiation patterns of 2×2 element planar array and single element equilateral triangular patch microstrip antennas forA= 1.0.
P-mode
Ept= 2hβpωp2/3aω0ε0(ω02−ωp2)
×exp(−¡βpr)/r×exp(−¡βpasinθcosφ/√ 3)
×1
4 × sin{βp·dx·sinθ·cosφ+βx} sin{0.5(βp·dx·sinθcosφ+βx)}
× sin{βp·dy·sinθ·sinφ+βy}
sin{0.5(βp·dy·sinθ·sinφ+βy)} ×[Epx+Epy], (4) where
ψx=βe·dx·sinθ·cosφ+βx, ψy=βe·dy·sinθ·sinφ+βy.
M andN are the elements placed along thex-axis andy-axis respectively,βxand βyare the progressive phase excitation difference along thex- andy-directions,Eθt
andEφtare the components of total electric field vectors for EM-mode,Eptis the total electric field vector for P-mode, Fx and Fy are the vector electric potentials for x- andy-components, respectively, Epx and Epy are the P-mode electric field vectors for x- and y-components, βe is the phase propagation constant for EM- mode given by 2πA/λ0,βp is the phase propagation constant for P-mode given by βec/v, wherecis the velocity of light andvis the root mean square thermal velocity of electron. A is the plasma frequency parameter given by (1−ωp2/ω02)1/2, where ω0, ωp are the angular source and plasma frequency,η0is the free space impedance equal to 120πohms.
3. Field patterns
The expression for total field patternR(θ, φ) is obtained as
R(θ, φ) =|Eθt|2+|Eφt|2. (5)
Figure 3. E-plane radiation patterns of 2×2 element planar array and single element equilateral triangular patch microstrip antennas forA= 0.5.
Figure 4. H-plane radiation patterns of 2×2 element planar array and single element equilateral triangular patch microstrip antennas forA= 1.0.
The values of Re and Rh are calculated by taking f = 10 GHz, a = 1.3 cm, dx=dy =λ/2 = 1.5 cm,n= 1, εr= 2.32 and the phase differenceβx=βy=π/2 and π/3. The results are plotted in figures 2 and 4 for two different planes (φ= 0 andφ=π/2) forA= 1.0, i.e. in free space and in figures 3 and 5 for two different planes (φ= 0 and φ=π/2) forA = 0.5, i.e. in a plasma medium. The P-mode fields are plotted in figure 6 for A = 0.5 for a limited range of 10◦ (from 50◦ to 60◦). The field patterns are also compared with single element triangular patch microstrip antenna. The calculated values of different pattern characteristics of array geometry for both the planes, i.e. φ= 0 andφ=π/2 and forβx=βy =π/2 andπ/3 are given in table 1.
4. Conclusions
From the above study, it is observed that there is a significant change in the radi- ation characteristics of the array geometry under investigation due to (i) variation of progressive phase excitation difference among the elements and (ii) variation of ratio of plasma to source frequency.
Figure 5. H-plane radiation patterns of 2×2 element planar array and single element equilateral triangular patch microstrip antennas forA= 0.5.
Figure 6. Plasma-mode field pattern of 2×2 element planar array and single element equilateral triangular patch microstrip antennas forA= 0.5.
Finally, it is concluded that the 2×2 element planar array of equilateral triangular patch microstrip antenna has unique radiation characteristics and a possible use of the present array geometry may be in search and track applications in radar system due to its unique scanning capabilities. The theoretical results obtained in the present study may be helpful for prospective antenna designers and investigators for several applications. An experimental verification of the present array geometry
Table 1. Calculated values of pattern characteristics of planar array antenna in free space.
φ= 0 plane φ=π/2 plane
2×2 Element planar array βx=βy=π/2 βx=βy=π/3 βx=βy=π/2 βx=βy=π/3
Half-power beam width 80◦ 60◦ 80◦ 60◦
(HPBW)
First null beam width 120◦ 100◦ 120◦ 100◦
(FNBW)
Direction of max. radiation 90◦ 90◦ 90◦ 90◦
[5] C A Balanis,Antenna theory – analysis and design(Harper and Row, New York, 1982) [6] J R James and P S Hall, Handbook of microstrip antennas (Peter-Peregrinus Ltd,
London, UK, 1989)
